Energy conversion

In this section, we first present a comprehensive study of single GaN NWs operated as photoconductors. Then, the application of In-containing NWs structures to photovoltaics is discussed; finally, we analyze the performance of GaN and InN NWs as piezoelectric converters for energy harvesting.

Photoconductive detection

The photodetector capabilities of single NWs are under study for a variety of materials, such as Si (Zhang et al. 2008; Alvarez et al. 2011), Ge (Kim 2010b), GaAs (Schricker et al. 2006); ZnO (Soci et al. 2007; Chen et al. 2010b; Peng et al. 2011), ZnTe (Cao et al. 2011), CdS (Gu and Lauhon 2006), or SnO2 (Hu et al. 2011). Focusing on III-nitrides, a number of publications address the behavior of single GaN NWs as photoconductors (Calarco et al. 2005; Polenta et al. 2008; Richter et al. 2008; Chen et al. 2007, 2008; Sanford et al. 2010; Rigutti et al. 2010b; De Luna Bugallo et al. 2011; Gonzalez-Posada et al. 2012, 2012b).

For a correct interpretation of the NW performance, structural parameters such as growth axis, crystallographic orientation of the sidewalls, NW diameter, and doping level are particularly relevant. Indeed, the angle between the polarization vector and the NW growth axis determines the internal electric field in heterostructured NWs, and the distribution of surface states and Fermi-level pinning at the sidewall facets has an impact on the free carrier distribution in the NWs, due to their large surface-to-volume ratio. In the case of GaN NWs, surface states induce an upwards band bending at the surface that can result in a total depletion of the NW. Applying the abrupt depletion approximation to a cylindrical structure (Luscombe and Frenzen 2002; Dobrokhotov et al. 2006; Sanford et al. 2010), total depletion occurs for an NW radius

where ee0 are the dielectric constant and the permitivity of vacuum, Ф is the surface potential (conduction band edge—Fermi level), e is the electron charge, and Nd is the doping level.

In this section, and unless indicated, we focus on (000-1)-oriented NWs with {10-10} m-plane sidewall facets, which is the most common crystallographic configuration for self-assembled NWs grown by PAMBE or MOCVD. For the fabrication of single-NW devices, NWs are generally detached from their original substrate and dispersed on SiO2/Si or SiNK plates, and contacted by e-beam lithography.

Dark current. Figure 9.7 compares typical current-voltage (I-V) curves of single n-i-n and undoped (000-1)-oriented NWs with a diameter of « 50 nm,

Left: I-V characteristics at room temperature of single n-i-n and undoped NWs measured at room temperature in the dark and under UV illumination. Right

Fig. 9.7. Left: I-V characteristics at room temperature of single n-i-n and undoped NWs measured at room temperature in the dark and under UV illumination. Right: Top-view SEM image of an n-i-n (top) and undoped (bottom) contacted single NW. Black symbols correspond to the dark current; grey symbols correspond to illumination with « 0.2 W/cm2 of UV light (A = 244 nm). (Reprinted from Gonzalez-Posada et al. (2012b).) measured in the dark (in the air and in vacuum) and under ultraviolet (UV) illumination (in the air). N-i-n structures consist of two Si-doped n-type edges and an undoped middle section with a nominal length of 400 nm. Focusing on the characteristics in the dark, we observe a strong dependence of the dark current on the measurement atmosphere. Measurements in the air render current levels one order of magnitude lower than in vacuum (Bertness et al. 2011; Gonzalez-Posada et al. 2012b), in agreement with results in CdS NWs (Gu and Lauhon 2006). In the dark, n-i-n NWs present the I a (a > 2) behavior characteristic of space-charge-limited transport, as expected due to the surface-induced depletion of the non-intentionally-doped sections.

Space-charge-limited current was first studied in insulators, where it is the dominant mechanism when the charge injected by the electrodes exceeds the free carrier density in the intrinsic material. In ideal insulators the I — V curve presents a characteristic I 2 dependence (Mott-Gurney law) (Rose 1955; Lampert 1956). However, in low-dimensional materials such as NWs, the presence of surface states leads to I a with a > 2 (Gu and Lauhon 2006). In the literature, space-charge-limited current is observed for undoped GaN NWs with diameters below 100 nm (Calarco et al. 2005, 2011; Sanford et al. 2010; Gonzalez- Posada et al. 2012). Space-charge-limited current has also been reported as the dominant transport mechanism in undoped CdS (Gu and Lauhon 2006), GaAs (Schricker et al. 2006), or ZnO (Soci et al. 2010) NWs.

On the other hand, undoped NWs in Fig. 9.7 present current densities at least two orders of magnitude lower than n-i-n devices. The approximately linear I—V characteristic is explained by the trap-filling process characteristic of insulators prior to the application of the voltage (Lampert 1956). Under illumination, undoped NWs display larger on/off current contrast in comparison to n-i-n NWs. However, the overall photocurrent level in undoped NWs is smaller by at least one order of magnitude.

Light absorption and polarization. In general, the coupling of the light into the NW can be confirmed by analyzing the photoresponse as a function of the polarization angle, 9, when exciting with linearly polarized light. The absorption properties of semiconducting NWs are strongly dependent on the polarization of the incident radiation. The two major mechanisms responsible for this phenomenon are (i) the modification of energy distribution by size quantization (Peter and Kerry 1990; Xinyuan et al. 2004), and (ii) the dielectric confinement of the optical electric field due to the difference in the dielectric constants of the NW, eNW, and the environment, eenv (Maslow et al. 2006; Ruda and Shik 2005; Gonzalez-Posada et al. 2012). While the former mechanism is significant only in very thin NWs (diameter < 10 nm), the relevance of the latter is dictated by the eNW /?env ratio, though it has to be treated differently if the NW diameter is much smaller than the light wavelength. In the case of thin NWs (diameter < 100 nm), due to the suppression of the perpendicular component of the electric field vector inside the NW, the ratio of the absorption coefficient for light polarization parallel and perpendicular to the NW axis is given by (Ruda and Shik 2005)

This theoretical ratio is about 30 for GaN. For thicker NWs the non-uniform distribution of the field inside the NW must also be taken into account, and the k///k± ratio becomes strongly dependent on the excitation wavelength.

The inset in Fig. 9.8 presents the photocurrent from a single NW exposed to linearly polarized UV light (Gonzalez-Posada et al. 2012). The anisotropy of the optical absorption results in the photocurrent varying as I = I0cos(2e), where в is the light polarization angle with respect to the NW axis (Maslow et al. 2006).

Linearity, gain, and spectral response. The quantitative analysis of the photoresponse requires an assessment of the linearity of the device with the impinging optical power, P. Figure 9.8 presents the results of the characterization performed under continuous-wave (CW) illumination, as well as at different light-chopping frequencies. The photocurrent scales sublinearly with P following approximately a power law I e with в < 1, though both the photocurrent magnitude and the value of в depend on the frequency. A sublinear response with the optical power has been reported in NWs based on other materials, such as Si (Zhang

Photocurrent variation from a single NW as a function of the excitation power (A = 244 nm) and frequency. Inset

Fig. 9.8. Photocurrent variation from a single NW as a function of the excitation power (A = 244 nm) and frequency. Inset: Photocurrent dependence with the polarization angle of a linearly polarized white-light source and simulated angle dependence for a NW, following the I ж cos(2e) proportionality. (Reprinted with permission from Gonzalez-Posada et al. (2012), © 2012 American Chemical Society.)

et al. 2008), Ge (Kim et al. 2010b), ZnO (Soci et al. 2007; Chen et al. 2010b), SnO2 (Hu et al. 2011), or ZnTe (Cao et al. 2011). This strong non-linearity, also comparable to observations in GaN 2D photoconductors (Monroy et al. 2003), is generally associated with high gain, persistent photoconductivity effects, and a strong photoresponse to excitation below the GaN band gap. The photodetector gain, G, defined as the number of electrons detected per absorbed photon, can be estimated from the photocurrent, I, via the equation:

where h is Planck’s constant, c is the speed of light, and A is the excitation wavelength. Note that this equation provides an underestimation of G, since it assumes the detector internal quantum efficiency to be unity, i.e. the light reflected or transmitted through the NW is neglected. Taking the NW size into account, G reaches values of 106 —107 for an irradiance of 0.2 mW/cm2.

The magnitude of G can vary as a function of the measuring atmosphere and the doping profile in the NW. Whereas for n-i-n NWs gain measurements in vacuum and in the air are in the same range (±5%), for undoped NWs the gain measured in vacuum can be more than one order of magnitude higher than in the air. Despite the enhancement of the photocurrent in vacuum, its sublinear behavior with the optical power remains unchanged, i.e. в remains constant within an error bar ±5%. A similar enhancement of the photoresponse in vacuum has been reported in ZnO NWs (Soci et al. 2007).

Figure 9.9 presents the spectral photoresponse of a single GaN NW (n-i-n or undoped, samples grown by PAMBE) measured by the lock-in technique at various frequencies. The photocurrent spectra present a flat spectral response for wavelengths above the GaN band gap (A < 350 nm), while the response to A > 450 nm is below the resolution limit of the system (Gonzalez-Posada et al. 2012, 2012b). Similar results are obtained in the case of MOCVD-grown GaN NWs (De Luna Bugallo et al. 2011). In order to verify the NW blindness to visible light, they were exposed to 0.5W/cm2 of the 488 nm line of an Ar laser. The NWs show no sensitivity to this illumination, neither under CW illumination nor at different chopping frequencies (2—100 Hz), which confirms a UV (350-nm)/visible (488 nm) contrast of more than six orders of magnitude. This result sets a critical difference in performance with GaN 2D photoconductors, whose visible rejection ratio decreases markedly when decreasing the measuring frequency, to the point of being lower than one decade for CW measurements (Monroy et al. 2003). This poor visible rejection of GaN 2D photoconductors, orders-of-magnitude worse than expected from the spectral variation of the GaN absorption coefficient, is explained by the fact that the photocurrent gain is associated with charge separation at extended defects. In the case of GaN NWs, the huge UV/visible contrast is understood as a result of the absence of extended defects, except for the surface dangling bonds. Furthermore, the NW sidewalls are {10-10} m-planes, whose dangling bonds do not create occupied states within

Spectral response of a single NW under 3 V bias at a measurement frequency of 2—1000 Hz

Fig. 9.9. Spectral response of a single NW under 3 V bias at a measurement frequency of 2—1000 Hz. Data are corrected by the lamp emission spectrum, taking the sublinear power dependence of the NW into account. (Reprinted, with permission, from Gonzalez-Posada et al. (2012), © 2012, American Chemical Society.)

the band gap (Van de Walle and Segev 2007). The cutoff wavelength can be shifted into the visible spectral range by incorporating InGaN insertions in the NW structure (De Luna Bugallo et al. 2011).

Time response. N-i-n NWs present non-exponential dynamics with an initial decay constant around 4-10 ms independent of the measuring environment (Gonzalez-Posada et al. 2012). In the case of undoped NWs, their behavior is similar to n-i-n devices when operated in the air, but persistent photoconductivity effects in the range of tens to hundreds of seconds are activated under vacuum (Gonzalez-Posada et al. 2012b).

Photodetection mechanism. Under illumination, we observe a variation of the NW conductivity Да. Keeping in mind that the conductivity is given by а = enp, where n is the carrier density and p is the carrier mobility, a change in conductivity, Да = е(рДп + пДр), can occur either due to change in the carrier concentration, Дп, or to a change in the carrier mobility, Др. The carrier concentration should scale linearly with the excitation, in contrast with the observed non-linear behavior of the photocurrent. Moreover, the carrier lifetime measured by PL in the ns range (Pfiiller et al. 2010) is in contradiction with the photocurrent decay times described above (millisecond times for n-i-n NWs and significantly longer for undoped NWs). We can hence conclude that the photodetector response is dominated by Др, which is affected by the band bending induced by the surface and by the scattering associated with surface states (Gonzalez- Posada et al. 2012b). Thus, the non-linear photocurrent gain in NWs is assigned to hole-trapping at surface states (Calarco et al. 2005; Soci et al. 2010), which results in a spatial separation of the electron and hole. When light is switched off, photogenerated carriers recombine at a non-exponential rate, due to the time-dependent potential barrier associated with the surface band bending. The current recovery involves also a rearrangement of the surface charge, which is at the origin of the slow photocurrent components. The recombination process is accelerated in presence of adsorbed oxygen, which decreases the carrier lifetime (Reshchikov et al. 2009; Foussekis et al. 2009; Pfuller et al. 2010).

The different response of n-i-n NWs and undoped NWs is assigned to the different location and behavior of the Fermi level at the surface. Surface states play a major role on the undoped NW photocurrent dynamics due to the unpinned Fermi level at the clean m-plane surfaces (Carterm and Stampflm 2009; Bertelli et al. 2009). In the case of n-i-n NWs, the pinning of the Fermi level close to the conduction band at the n-regions and the reduction of the surface potential due to residual silicon on the sidewalls reduce the photoinduced sweep of the Fermi level, preventing persistent effects and reducing the environment sensitivity. Therefore, an important projection of the present work is that the doping profile of the NW is a parameter critical for determining not only its performance as a photodetector, but also its functionalization capabilities for use as a chemical sensor.

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